We have presented a synthetic design for a circuit that performs
inference. But how would one “reverse-engineer” a natural circuit
that performed a similarly sophisticated computation? A line of work by neuroscientists and molecular biologists has pointed
to cases where measuring input-output relationships of a dynamic and stateful
system (whether biological [1]} or synthetic [2]}, [3]}, [4]}), without a sufficiently detailed theoretical framework in
which to interpret these measurements, can lead to potentially misleading descriptions of how the underlying system
works. In systems biology, a common approach to studying cellular
pathways (enabled in part by high-throughput measurement technologies developed in recent years) has been to quantitatively
measure a pathway's component of interest as a function of
a quantitatively varying environmental input. When multiple inputs are
varied along a sufficiently large dynamic range, this measurement can
reveal surprising relationships between inputs and
outputs. For example, [5]} measured the level of
induction of the galactose metabolic pathway (Gal) in yeast cells
grown in different concentrations of glucose (which represses Gal) and galactose (which
activates Gal) and found that Gal induction depends on the ratio of
glucose to galactose. These experiments are premised on obtaining
steady-state-like conditions where the level of the sugars (glucose
and galactose) and measured signal are relatively stable.
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